A178339 Primes p such that the sum of decimal digits of p divides the product of decimal digits of p+1 and that product is nonzero.

11, 13, 17, 211, 233, 277, 367, 431, 457, 523, 541, 547, 587, 727, 743, 761, 853, 857, 1153, 1223, 1373, 1447, 1483, 1531, 1571, 1627, 1663, 1733, 1861, 2141, 2213, 2251, 2273, 2293, 2347, 2383, 2411, 2437, 2473, 2521, 2617, 2657, 2741, 2833, 2851, 3221, 3371

Offset

1,1

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Example

2+3+3 = 8 divides 2*3*4 = 24, so 233 is a member.

Maple

A178339 := proc(n) option remember: local p, q: if(n=1)then return 11: fi: p:=procname(n-1): do p:=nextprime(p): q:=mul(d, d=convert(p+1, base, 10)): if(q>0 and q mod add(d, d=convert(p, base, 10)) = 0)then return p: fi: od: end: seq(A178339(n), n=1..47); # Nathaniel Johnston, May 27 2011

Mathematica

fQ[n_] := Block[{s = Plus @@ IntegerDigits@n, p = Times @@ IntegerDigits[n + 1]}, Mod[p, s] == 0 && p > 0]; Select[ Prime@ Range@ 250, fQ@# &]; Select[ Prime@ Range@ 500, fQ@# &]
Select[Prime[Range[500]], DigitCount[#+1, 10, 0]==0&&Divisible[Times@@IntegerDigits[ #+1], Total[ IntegerDigits[#]]]&] (* Harvey P. Dale, May 24 2023 *)

Crossrefs

Sequence in context: A098031 A179208 A098423 * A088561 A211457 A154523

Adjacent sequences: A178336 A178337 A178338 * A178340 A178341 A178342

Keyword

base,easy,nonn

Author

Giovanni Teofilatto, May 25 2010

Extensions

Corrected and extended by Robert G. Wilson v, Jun 05 2010

Name corrected by Nathaniel Johnston, May 27 2011

Status

approved